https://github.com/javierbarbero/DataEnvelopmentAnalysis.jl
Tip revision: e42f208
deaprofit.jl
``````# This file contains functions for the Profit Efficiency DEA model
"""
ProfitDEAModel
An data structure representing a profit DEA model.
"""
struct ProfitDEAModel <: AbstractProfitDEAModel
n::Int64
m::Int64
s::Int64
Gx::Symbol
Gy::Symbol
monetary::Bool
dmunames::Union{Vector{String},Nothing}
eff::Vector
lambda::SparseMatrixCSC{Float64, Int64}
techeff::Vector
alloceff::Vector
normalization::Vector
Xtarget::Matrix
Ytarget::Matrix
end

"""
deaprofit(X, Y, W, P; Gx, Gy)
Compute profit efficiency using data envelopment analysis model for
inputs `X`, outputs `Y`, price of inputs `W`, and price of outputs `P`.

# Direction specification:

The directions `Gx` and `Gy` can be one of the following symbols.
- `:Zeros`: use zeros.
- `:Ones`: use ones.
- `:Observed`: use observed values.
- `:Mean`: use column means.
- `:Monetary`: use direction so that profit inefficiency is expressed in monetary values.

Alternatively, a vector or matrix with the desired directions can be supplied.

# Optional Arguments
- `names`: a vector of strings with the names of the decision making units.

# Examples
```jldoctest
julia> X = [1 1; 1 1; 0.75 1.5; 0.5 2; 0.5 2; 2 2; 2.75 3.5; 1.375 1.75];

julia> Y = [1 11; 5 3; 5 5; 2 9; 4 5; 4 2; 3 3; 4.5 3.5];

julia> P = [2 1; 2 1; 2 1; 2 1; 2 1; 2 1; 2 1; 2 1];

julia> W = [2 1; 2 1; 2 1; 2 1; 2 1; 2 1; 2 1; 2 1];

julia> deaprofit(X, Y, W, P, Gx = :Monetary, Gy = :Monetary)
Profit DEA Model
DMUs = 8; Inputs = 2; Outputs = 2
Returns to Scale = VRS
Gx = Monetary; Gy = Monetary
─────────────────────────────────────
Profit     Technical    Allocative
─────────────────────────────────────
1     2.0   0.0           2.0
2     2.0  -5.41234e-16   2.0
3     0.0   0.0           0.0
4     2.0   0.0           2.0
5     2.0   0.0           2.0
6     8.0   6.0           2.0
7    12.0  12.0          -1.77636e-15
8     4.0   3.0           1.0
─────────────────────────────────────
```
"""
function deaprofit(X::Union{Matrix,Vector}, Y::Union{Matrix,Vector},
W::Union{Matrix,Vector}, P::Union{Matrix,Vector};
Gx::Union{Symbol,Matrix,Vector}, Gy::Union{Symbol,Matrix,Vector},
monetary::Bool = false,
names::Union{Vector{String},Nothing} = nothing,
optimizer::Union{DEAOptimizer,Nothing} = nothing)::ProfitDEAModel

# Check parameters
nx, m = size(X, 1), size(X, 2)
ny, s = size(Y, 1), size(Y, 2)

nw, mw = size(W, 1), size(W, 2)
np, sp = size(P, 1), size(P, 2)

if nx != ny
throw(DimensionMismatch("number of rows in X and Y (\$nx, \$ny) are not equal"));
end
if nw != nx
throw(DimensionMismatch("number of rows in W and X (\$nw, \$nx) are not equal"));
end
if np != ny
throw(DimensionMismatch("number of rows in P and Y (\$np, \$ny) are not equal"));
end
if mw != m
throw(DimensionMismatch("number of columns in W and X (\$mw, \$m) are not equal"));
end
if sp != s
throw(DimensionMismatch("number of columns in P and Y (\$sp, \$s) are not equal"));
end

# Build or get user directions
if typeof(Gx) == Symbol
Gxsym = Gx

if Gx == :Zeros
Gx = zeros(size(X))
elseif Gx == :Ones
Gx = ones(size(X))
elseif Gx == :Observed
Gx = X
elseif Gx == :Mean
Gx = repeat(mean(X, dims = 1), size(X, 1))
elseif Gx == :Monetary
GxGydollar = 1 ./ (sum(P, dims = 2) + sum(W, dims = 2));
Gx = repeat(GxGydollar, 1, m);
else
throw(ArgumentError("Invalid `Gx`"));
end

else
Gxsym = :Custom
end

if typeof(Gy) == Symbol
Gysym = Gy

if Gy == :Zeros
Gy = zeros(size(Y))
elseif Gy == :Ones
Gy = ones(size(Y))
elseif Gy == :Observed
Gy = Y
elseif Gy == :Mean
Gy = repeat(mean(Y, dims = 1), size(Y, 1))
elseif Gy == :Monetary
GxGydollar = 1 ./ (sum(P, dims = 2) + sum(W, dims = 2));
Gy = repeat(GxGydollar, 1, s);
else
throw(ArgumentError("Invalid `Gy`"));
end

else
Gysym = :Custom
end

if (size(Gx, 1) != size(X, 1)) | (size(Gx, 2) != size(X, 2))
throw(DimensionMismatch("size of Gx and X (\$(size(Gx)), \$(size(X))) are not equal"));
end
if (size(Gy, 1) != size(Y, 1)) | (size(Gy, 2) != size(Y, 2))
throw(DimensionMismatch("size of Gy and Y (\$(size(Gy)), \$(size(Y))) are not equal"));
end

# Default optimizer
if optimizer === nothing
optimizer = DEAOptimizer(:LP)
end

# Get maximum profit targets and lambdas
n = nx

Xtarget, Ytarget, plambdaeff = deamaxprofit(X, Y, W, P, optimizer = optimizer)

# Profit, technical and allocative efficiency
maxprofit = sum(P .* Ytarget, dims = 2) .- sum(W .* Xtarget, dims = 2)

pefficiency  = vec(maxprofit .- ( sum(P .* Y, dims = 2) .- sum(W .* X, dims = 2)))
normalization = vec(sum(P .* Gy, dims = 2) .+ sum(W .* Gx, dims = 2))
techefficiency = efficiency(deaddf(X, Y, Gx = Gx, Gy = Gy, rts = :VRS, slack = false, optimizer = optimizer))

if monetary
techefficiency = techefficiency .* normalization
else
pefficiency = pefficiency ./ normalization
end

allocefficiency = pefficiency - techefficiency

return ProfitDEAModel(n, m, s, Gxsym, Gysym, monetary, names, pefficiency, plambdaeff, techefficiency, allocefficiency, normalization, Xtarget, Ytarget)

end

function Base.show(io::IO, x::ProfitDEAModel)
compact = get(io, :compact, false)

n = nobs(x)
m = ninputs(x)
s = noutputs(x)
dmunames = names(x)

eff = efficiency(x)
techeff = efficiency(x, :Technical)
alloceff = efficiency(x, :Allocative)

if !compact
print(io, "Profit DEA Model \n")
print(io, "DMUs = ", n)
print(io, "; Inputs = ", m)
print(io, "; Outputs = ", s)
print(io, "\n")
print(io, "Returns to Scale = VRS")
print(io, "\n")
print(io, "Gx = ", string(x.Gx), "; Gy = ", string(x.Gy))
print(io, "\n")
show(io, CoefTable(hcat(eff, techeff, alloceff), ["Profit", "Technical", "Allocative"], dmunames))
end

end
``````